As Apple announced record profits, chief executive Tim Cook confirmed that even supplies of older, cheaper models of the iPhone were not enough to satisfy demand, and that sales of iMacs fell primarily because the company could not make the new design fast enough. He added that iPad Mini demand, too, continued to outstrip supply as consumers flocked to the device that Apple’s Steve Jobs had said the company should never make.

“If you look at the iPhone sales across the quarter, we were very constrained for much of the quarter on iPhone 5. As we begin to produce more and ship more, sales went up. iPhone 4 was actually in constraint for the entire quarter. Sales remained strong. That’s how sales progressed along the quarter,” said Cook. Overall, the iPhone provides 56pc of Apple’s revenue.

Mr Cook also downplayed the prospect of new products: ““We’re not interested in revenue for revenues’ sake,” he said. “We could put the Apple brand on a lot more stuff, but we don’t want to do that.”

The company sold a record 47.8m iPhones, helped by the launch of the iPhone 5 in September. Sales of the iPad reached 22.9m, eclipsing the 22.4m that had been forecast. Sales of iPods also beat forecasts as consumers snapped up 12.7m of them.

Overall revenues for the quarter were $54.5bn, 18pc higher than the same quarter in 2011, and Apple announced record profits of $13.1bn. It also announced, however, that the next quarter would likely provide sales of $41-$43bn, down from Wall Street hopes of at least $45bn.

On the earnings call after the announcement of the results, Mr Cook said “we believe we can achieve a supply/demand balance on iPad Mini and on iPhone 4 during this quarter”, indicating that the two-generations old iPhone remains consumers’ cheapest route into Apple’s range, and implicitly playing down rumours that the company might make a cheaper model.

The iPhone 4 retails for $200 or £110 less than the current iPhone 5.

Apple’s shares have fallen by nearly a third in recent months, and took a further pummeling after the latest results, as it struggles to retain its reputation for innovation. Launching the iPhone in 2007, Steve Jobs claimed it would take rivals five years to catch up. Six years on, traders appear to believe they have, even though Apple continues to generate huge profits.

Mr Cook didn’t explicitly rule out a cheaper model, which could appeal to the burgeoning Chinese market but risks diluting Apple’s valuable brand. He said that he thought the current 4” screen size, however, was the correct choice, despite a trend for larger phones running the rival Google Android operating system. “We put a lot of thinking into screen sizes and we believe we’ve picked the right one,” he said.

Mr Cook added that “The most important thing to Apple is to make the best products in the world that enrich customers lives. That’s our high-order bit. That means that we aren’t interested in revenue for revenues sake. That’s not what we’re here for. We want to make only the best products.” The frequently repeated sentiment is not what many investors wanted to hear.

Mr Cook did, however, offer some hope on one long-awaited TV product: “I have said in the past this is an area of intense interest for us,” he said. “It remains that. There is a lot we can contribute in this space. I don’t want to be more specific.”